Why is the Turing test so popular?
Because it is:


Easy to explain. (Its essentially a game, the "imitation game")
Intuitively plausible as a metric.
The idea of "people v.s. AI" is very marketable.
At the time we thought that we can analyze cognition strictly in terms of input/output (per behaviorism). Cognitivism, embodied cognition, developmental cognition are all sub-fields that have a right to challenge the Turing Test, but they weren't developed at the time of Turing.


Of course, it also helps that Turing is a very important figure in AI/CS.